Math Corner

Logic, often translated as thought or reason, builds the foundation for critical thinking skills. It is essential for success in higher level math, computer science, philosophy, science, engineering problem solving and decision-making. Logic demands that each statement be supported by reason. In logic puzzles, each conclusion can be supported by a “because” statement. At higher levels, students begin to use ‘if…then…” statements to support their conclusions. ​Logic puzzles require students to practice using both deductive and inductive reasoning skills. Deductive reasoning is the practice of using information from a larger set of information to understand other sets of related information. Inductive reasoning is the practice of using specific data to draw a much larger conclusion. These skills will prove indispensable as children emerge in their professional and academic lives.

FREEBIE: Binary Puzzle Sample

In the United States, formal training in logic is often limited to writing formal proofs in high school geometry classes. Yet, logic can easily be introduced to younger students through fun games and puzzles. ​

Logic through Binary Puzzles

The key to teaching students logic through games and puzzles is to train them to consistently explain “why” they are able to make each of their moves. I train them to precede each move with a statement in the form of:

“I know ________________ because ______________________.”​Students are not allowed to make moves if they “think” something is true or if something “could” be true.I always start with Binary Puzzles because the rules are very simple. Each puzzle is a square array with some cells containing 1s or 0s. The goal is to fill in the empty cells using the following rules:

Each row must have the same number of 1s as 0s

Each column must have the same number of 1s as 0s.

Three 1s can’t be next to each other in any row or column.

Three 0s can’t be next to each other in any row or column.

In order to discuss our example puzzle, we will label each column and row so we can easily identify each cell. So in the example below, there is a 1 in cell Aa and a 0 in cell Bd.

Children typically try to start from the top of a puzzle and work their way down. So a child is likely to start with cell Ab. This cell “Could” contain a 0. But it also “Could” contain a 1. We really can’t use any of the four rules to know for certain what this cell contains.

Look at cell Ac. This cell can’t be a “0” because putting a “0” in this cell would violate Rule #4. So we can say:

“I know that cell Ac is a 1 BECAUSE rule #4 says that we can’t have three 0s next to each other in any column.”

Notice how this statement is supported by one of the rules.

Look at the updated puzzle. What other cells can you find based on the rules of the puzzle?

​You should be able to make the following statements:

“I know that cell Ab is a 0 BECAUSE rule #3 says that we can’t have three 1s next to each other in any row."

“I know that cells Af and Df are 0s BECAUSE rule #3 says that we can’t have three 1s next to each other in any column.”

“I know that cells Bb, Be, Ca, Cd, Ec, and Fe are 1s BECAUSE rule #4 says we can’t have three 0s next to each other in any row."

Update the puzzle for each of these statements then use the additional information to try to fill in more spaces.

Based on this updated puzzle you should be able to make the following statements:

“I know that cell Ae contains a 1 BECAUSE rule #1 says that each row must have the same numbers of 1s as 0s and there are already three 0s in that row.’

“I know that cells Ba and Ce contain 0s BECAUSE rule #1 says that each row must have the same numbers of 1s as 0s and there are already three 1s in those rows.’

“I know that cells Db and Ef contain 1s BECAUSE rule #2 says that each column must have the same number of 1s as 0s and there are already three 0s in those columns.”​“I know that cell Dd contains a 0 BECAUSE rule #2 says that each column must have the same number of 1s as 0s and there are already three 1s in column d.”

After filling in these cells, you should be able to easily finish the puzzle.

Review each rule to make sure that your puzzle is correct:

Confirm that each row contains three 0s and three 1s.

Confirm that each column contains three 0s and three 1s.

Scan each row and column to make sure that there are no instances where three 0s or three 1s are next to each other.

Now try some on your own. Remember “No Guessing in Logic.” You must be able to support each move with one of the rules before writing a 1 or 0 in a cell.

​Did you like this puzzle? Download more binary puzzles!

(Set B) Binary Puzzles (6 x 6)

$1.00

Binary Puzzles are the perfect introduction to logic. Students only need to know how to count to three to complete these logic puzzles! Each puzzle is a square array with cells containing 1s and 0s. Fill in the empty cells using the following rules:​

(Set A) Binary Puzzles (6 x 6)

$1.00

Binary Puzzles are the perfect introduction to logic. Students only need to know how to count to three to complete these logic puzzles! Each puzzle is a square array with cells containing 1s and 0s. Fill in the empty cells using the following rules:​

(Set A) Binary Puzzles (8 x 8)

$1.00

Binary Puzzles are the perfect introduction to logic. Students only need to know how to count to three to complete these logic puzzles! Each puzzle is a square array with cells containing 1s and 0s. Fill in the empty cells using the following rules:​

(Set B) Binary Puzzles (8 x 8)

$1.00

Binary Puzzles are the perfect introduction to logic. Students only need to know how to count to three to complete these logic puzzles! Each puzzle is a square array with cells containing 1s and 0s. Fill in the empty cells using the following rules:​

(Set A) Binary Puzzles (10 x 10)

$1.00

Binary Puzzles are the perfect introduction to logic. Students only need to know how to count to three to complete these logic puzzles! Each puzzle is a square array with cells containing 1s and 0s. Fill in the empty cells using the following rules:​

(Set B) Binary Puzzles (10 x 10)

$1.00

Binary Puzzles are the perfect introduction to logic. Students only need to know how to count to three to complete these logic puzzles! Each puzzle is a square array with cells containing 1s and 0s. Fill in the empty cells using the following rules:​